Advanced Mechanics Flashcards

The critical buckling load for a pin-pin column of length L, modulus E, and moment of inertia I is given by Euler's formula as:

Answer: π²EI/L²

Euler's critical load for a pin-pin column is P_cr = π²EI/L², corresponding to an effective length of L.

In a Mohr's circle construction, the center of the circle lies at:

Answer: ((σ_x + σ_y)/2, 0)

The center of Mohr's circle is at the average normal stress ((σ_x + σ_y)/2, 0) on the σ–τ plane.

Which statement correctly describes Saint-Venant's principle?

Answer: The effects of localized loads become negligible at distances large compared to the load region

Saint-Venant's principle states that the stress distribution away from the point of load application is independent of how the load is distributed, provided the resultant is the same.

For a linearly elastic material, the relationship between shear modulus G, Young's modulus E, and Poisson's ratio ν is:

Answer: G = E/(2(1+ν))

The elastic constants are related by G = E / [2(1 + ν)], valid for isotropic materials.

A stepped shaft transmits torque T. At a step where the radius changes sharply, the stress concentration factor K_t is used because:

Answer: Local geometry causes stress to exceed the nominal value

Geometric discontinuities like fillets and steps create local stress concentrations where actual stress = K_t × nominal stress.

The compatibility equations in elasticity theory ensure that:

Answer: The displacement field is single-valued and continuous

Compatibility equations guarantee that the strain field derived from stresses corresponds to a continuous, single-valued displacement field with no gaps or overlaps.

Creep in metals at elevated temperatures is best described as:

Answer: Time-dependent permanent deformation under constant stress

Creep is the slow, time-dependent plastic deformation that occurs under sustained stress, especially above ~0.4 T_m (homologous temperature).